# Inertia of a body

1. Apr 25, 2015

### Lim Heng Leng

I would appreciate someone's advice on the following question:

"An airplane was moving in the forward direction on the runway when it suddenly stopped. When the airplane stopped, some passengers who did not put on their seat belts fell forward from their seats.

Would a passenger of larger mass be more likely to fall further from his seat as compared to a passenger of smaller mass? Explain you answer."

My answer is "The passenger of larger mass is likely to fall further further from his seat. This is due to his larger mass and hence larger inertia which causes him to continue moving in the forward direction more than someone of a smaller mass."

Am I correct in my answer or are there other considerations that I must look at before arriving at my answer?

2. Apr 25, 2015

### paisiello2

Inertia only applies to acceleration not velocity. It is a body's resistance to a change in velocity.

So the simple answer is they would fall forward the same.

Now technically they are sitting on their seats which means there's going to be friction acting as they move forward. Since the friction force is proportional to the normal force then that means the larger passenger will see more friction. Therefore the smaller person should move further.

3. Apr 25, 2015

### Simon Bridge

Welcome to PF;
I'd like a bit more detail about why a more massive person falls further forward - saying they fall further because they have more inertia is begging the question. Since mass and inertia are the same thing you are just saying, "the person with the most inertia falls further because they have the most inertia" see?

paisiello2 has done you a favor by giving you a complete answer ... you should check that answer against your understanding to make sure you follow the reasoning and can see why it is more complete. We do not normally do these sorts of questions for you so you are lucky.
Note: friction is proportional to the mass, but higher mass makes it harder to stop.

I tend to be a tad perverse when I answer these questions - i.e. both passengers hit the back of the seat in front of them: aircraft seats tend to be close together.
The less massive passenger, being smaller, moves further as measured by displacement of their centers of mass. It is unusual for a less massive human to have similar dimensions to the more massive one... but that's probably not the kind of answer you are expected to give.

4. Apr 25, 2015

### Staff: Mentor

The standard thought experiment works well here: imagine two passengers of equal mass right next to each other. They certainly fall in the same way. What happens if they hold each other so they behave like a single passenger of twice the mass?